Such a vehicle seat is disclosed in document U.S. Pat. No. 4,192,545.
The strength member of the seat back described in that document comprises a generally U-shaped tube of constant circular section along its length, such that the mechanical performance of said back strength member is limited.
In particular, given the draconian safety standards presently in force for vehicle seats, a seat back strength member made in accordance with the teaching of the above-mentioned document and complying with the standards:
That would give rise to a seat back strength member that is relatively heavy and expensive.